Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26021210 | C2 | semidirect |
| 2. #26019038 | C2 | semidirect |
| 5. #26018608 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 177. C89 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021210 | 2 |
| #26019038 | 2 |
| #26018947 | 2 |
| #26018747 | 2 |
| #26018608 | 2 |
| #26018109 | 2 |
| C89×#3234 | 2 |
| #10509 | 89 |